# GMAT Math : Calculating the area of a square

## Example Questions

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### Example Question #58 : Quadrilaterals

Note: Figure NOT drawn to scale

Refer to the above figure, which shows Square  and Square . The ratio of  to  is 13 to 2. What is the ratio of the area of Square  to that of Square ?

Explanation:

To make this easier, assume that  and  - the reasoning generalizes. Then Square  has sidelength 15 and area . The sidelength of Square , each side being a hypotenuse of a right triangle with legs 2 and 13, is

.

The square of this, 173, is the area of Square .

The ratio is .

### Example Question #59 : Quadrilaterals

Note: Figure NOT drawn to scale

Refer to the above figure, which shows Square  and Square .  The ratio of  to  is 7 to 1.

Which of these responses comes closest to what percent the area of Square  is of that of Square ?

Explanation:

To make this easier, assume that  and ; the results generalize.

Each side of Square  has length 8, so the area of Square  is 64.

Each of the four right triangles has legs 7 and 1, so each has area ; Square  has area four times this subtracted from the area of Square , or

.

The area of Square  is

of that of Square .

Of the five choices, 80% comes closest.

### Example Question #61 : Quadrilaterals

The perimeter of a square is the same as the circumference of a circle with area 100. What is the area of the square?

Explanation:

The formula for the area of a circle is

.

If the area is 100, the radius is as follows:

The circle has circumference  times its radius, or

This is also the perimeter of the square, so the sidelength of the square is one-fourth this, or

The area of the square is the square of this, or

### Example Question #62 : Quadrilaterals

The perimeter of a square is the same as the circumference of a circle with radius 8. What is the area of the square?

The correct answer is not among the other choices.

Explanation:

A circle with radius 8 has as its circumference  times this, or

.

This is also the perimeter of the square, so the sidelength is one fourth of this, or

.

The area is the square of this, or

.

### Example Question #63 : Quadrilaterals

The perimeter of a square is the same as the length of the hypotenuse of a right triangle with legs 8 and 12. What is the area of the square?

The correct answer is not among the other responses.

Explanation:

The length of the hypotenuse of a right triangle with legs 8 and 12 can be determined using the Pythagorean Theorem:

Since this is also the perimeter of the square, its sidelength is one fourth of this, or

The area of the square is the square of this sidelength, or

### Example Question #21 : Squares

If the perimeter of a square is , what is its area?

Explanation:

The perimeter of a square, and any shape for that matter, is found by adding up all the exterior sides. Since all sides are equal in a square, we can say:

where  represents the length of a side

We can solve for the side length using the information provided:

The area of a square is found by squaring the side length:

### Example Question #65 : Quadrilaterals

The perimeter of a square is . Give its area.